Finite Group DatabasebetaFinite Group DatabasebetaOrder 21376.
712 conjugacy classes of subgroups; only the 149 normal subgroups are shown.
This group has 712 conjugacy classes of subgroups — too many to draw. Only its 149 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C2×#19128880 | C2 | semidirect |
| 2. C2×#19128852 | C2 | semidirect |
| 3. #24923847 | C2 | semidirect |
| 4. #24923430 | C2 | semidirect |
| 5. #24923423 | C2 | semidirect |
| 6. #24923413 | C2 | semidirect |
| 7. #24923406 | C2 | semidirect |
| 8. #24923271 | C2 | semidirect |
| 9. C2×#19128756 | C2 | semidirect |
| 10. #24923237 | C2 | semidirect |
| 11. C2×#137×C167 | C2 | semidirect |
| 52. #14581950 | D4 | semidirect |
| 86. C2×Q8×C167 | D4 | semidirect |
| 169. C167 | #3013 | semidirect |
| 172. C2×#137 | D167 | semidirect |
| 233. C2×Q8 | C22⋊D167 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#19128880 | 2 |
| C2×#19128852 | 2 |
| #24923847 | 2 |
| #24923430 | 2 |
| #24923423 | 2 |
| #24923413 | 2 |
| #24923406 | 2 |
| #24923271 | 2 |
| C2×#19128756 | 2 |
| #24923237 | 2 |
| C2×#137×C167 | 2 |
| #3013 | 167 |